How to find the function of this model?

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1 Answer
Barry H.
May 16, 2018

See below.

Explanation:

From the question, the distance between #p# and #r#, by Pythagoras, is #sqrt[x^2+9]# and the distance between #r# and #q# is #sqrt[[5-x]^2+16]#.

So the total cost #C# is will be #2[sqrt[x^2+9]]^2# +#3[sqrt[[5-x^2]+16]]^2#, this because the question tell us that the cost is dependent on the ' square' of the distance, and the 'square' of square root of a function is just the function. e.g, #[sqrt a]^2#=#a#.

Thus we have #C# =#2[x^2+9]# + #3[[5-x]^2+16]# and expanding the brackets in the expression,

#C# =#2x^2+18 #+ #3[25-10x+x^2+16]#,

=#2x^2+18+75-30x+3x^2+48#, and collecting like terms gives the expression in the question. Hope this helps.

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